Evaluating log-tangent integrals via Euler sums

An investigation into the representation of integrals involving the product of the logarithm and the arctan functions, reducing to log-tangent integrals, will be undertaken in this paper. We will show that in many cases these integrals take an explicit form involving the Riemann zeta function, the D...

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Bibliographic Details
Published inMathematical modelling and analysis Vol. 27; no. 1; pp. 1 - 18
Main Author Sofo, Anthony
Format Journal Article
LanguageEnglish
Published Vilnius Vilnius Gediminas Technical University 07.02.2022
Subjects
dirichlet beta functions
dirichlet lambda function
Dirichlet problem
euler sums
Functional equations
Functions
Integrals
log-tangent integral
Mathematical research
zeta functions
Australia
Euler sums
Dirichlet beta functions
zeta functions
Dirichlet lambda function
log-tangent integral
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Summary:An investigation into the representation of integrals involving the product of the logarithm and the arctan functions, reducing to log-tangent integrals, will be undertaken in this paper. We will show that in many cases these integrals take an explicit form involving the Riemann zeta function, the Dirichlet eta function, Dirichlet lambda function and many other special functions. Some examples illustrating the theorems will be detailed.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2022.13100